Verizon Wireless is feeling the crush of all of those LTE-enabled devices on its network.

The carrier said it is facing pressure to deliver increased amounts of bandwidth in big cities such as New York, San Francisco, and Chicago. In a rare admission on Tuesday, Verizon Chief Financial Officer Fran Shammo admitted the rapid growth in traffic was starting to hamper the quality of the service.

"There are certain pockets where we're absolutely going to experience that down tick from the LTE network down to 3G because of capacity constraints," Shammo said during an investor conference.

It's a surprising concession from a company that typically trumps its network superiority as a reason why customers should pay a premium for its wireless services. It has long touted itself as the nation's most reliable, but that claim has since been taken by AT&T, which also boasts the nation's fastest network. Verizon maintains it has the most reliable network, and cites a different study.

The growth in data traffic is a result of its early move into LTE. Verizon boasts the nation's largest LTE network, and the longest running, which has meant more LTE customers than anyone. And LTE customers like their data. While LTE customers make up a third of the company's total base, they consume 64 percent of the traffic.

The result has been a carrier struggling to keep up with data growth, something Shammo concedes has been tough. He said the carrier was taken by surprise in the growth in video traffic from LTE users. While he wouldn't say exactly how much more data an LTE user consumes versus a 3G customer, he said it was more than double. Relative to its competition, Shammo said Verizon was growing faster, so data consumption has likewise been accelerating.

Verizon isn't standing still. Shammo said the company has poured more money into the network, including increasing its capital expenditures by $500 million this year. The company is also investing in small cell technology and turning on more spectrum as it works to build up network capacity.

"By the end of this year you are going to see all those issues dissipate," Shammo said. "And then going into next year we will be ahead of the curve again."